# Oxford scientists discover why ketchup splatters from a nearly empty bottle

Ketchup is one of them The most popular seasoning In the US, along with mayonnaise, but getting those last few dollops out of the bottle often results in a sudden splatter. “It’s annoying, it’s potentially embarrassing, and it can ruin clothes, but can we do anything about it?” Calum Cattell of the University of Oxford said during a press conference earlier this week at the American Physical Society meeting on fluid dynamics in Indianapolis, Indiana. “More importantly, can understanding this phenomenon help us solve any other problems in life?”

The answer to both questions, according to Cuttle, is a A resounding yes. Together with his Oxford colleague, Chris McMinn, he conducted a series of experiments to determine the forces at play and to develop a theoretical model of ketchup mist. Among the more interesting results: Squeezing the bottle slower and doubling the diameter of the nozzle helps prevent splashing. There is also a critical threshold where the flow of ketchup suddenly goes from not splashing to splashing. a prepress sheet Published on arXiv and currently undergoing peer review.

Isaac Newton Defined properties for what he considered the “ideal fluid”. One of those characteristics is viscosity, loosely defined as the amount of friction/resistance to flow in a given material. Friction arises because a flowing fluid is essentially a series of layers sliding over one another. The faster one layer slides over the other, the greater the resistance, and the slower the layer slides over the other, the lower the resistance.

But not all fluids behave like Newton’s ideal fluid. In an ideal Newtonian fluid, viscosity depends largely on temperature and pressure: water will continue to flow—that is, behave like water—regardless of other forces acting on it, such as stirring or mixing. In a non-Newtonian fluid, viscosity changes in response to an applied stress or shear force, thus interfering with the boundary between fluid and solid behaviour. Physicists like to call this a “shear force”: moving a glass of water produces a shear force, and the water shears out of the way. The viscosity remains unchanged. But the viscosity of non-Newtonian fluids changes when shear force is applied.

Ketchup is a non-Newtonian liquid. Blood, yogurt, gravy, slush, pudding, and thick pie fillings are other examples, along with Hagfish slime. They are not quite alike in terms of their behaviour, but none of them adhere to Newton’s definition of an ideal fluid.

Ketchup, for example, consists of solid tomato powder suspended in a liquid, which makes it more of a “soft solid” than a liquid, to me Anthony Strickland of the University of Melbourne in Australia. The solids connect to create a continuous web, and one must overcome the strength of that web in order to get the ketchup to flow—usually by tapping or banging on the bottle. Once this happens, the viscosity decreases, and the lower it is, the faster the ketchup will flow. The scientists at Heinz set the optimal flow rate, or ketchup, at 0.0045 per hour.

When there is very little ketchup left in the bottle, you have to hit it harder, which increases the risk of it splattering. “By the time you get to the end, a lot of what’s inside is air,” Cattell said. “So when you squeeze, what you’re doing is compressing the air inside the bottle, which creates more pressure that pulls the bottle [ketchup] Outside. “The nozzle provides a viscous drag force corresponding to the viscous flow of ketchup, and the balance between them determines the rate of flow. As the bottle empties, the viscosity decreases because there is less ketchup to push out. More liquid means there is more room for air to expand inside the bottle, which reduces driving force over time. .

Understanding the complex dynamics of why a smooth stream suddenly turns into splatter begins by simplifying the problem. Cuttle and MacMinn created an analog of a ketchup bottle, filling syringes (essentially capillary tubes) with ketchup and then injecting different amounts of air (from 0 to 4 milliliters) at constant pressure rates to see how changing the amount of air affected the flow rate and whether the ketchup spattered. They repeated the experiments with syringes filled with silicone oil in order to better control viscosity and other key variables.

Result: Syringes containing 1 milliliter or more of air injected produce a spray. “This tells us you need some air in the syringe or bottle to generate spatter and create this unsteady flow of flow,” Cattell said. This constitutes a critical “ketchup splatter” threshold at which the ketchup goes from a smooth flow to a splatter, depending on factors such as the amount of air, the compression rate, and the diameter of the nozzle. Under this limit, the driving force and the fluid flow are balanced, so the flow is smooth. Above the threshold, the driving force decreases faster than the outflow. The air becomes hyper-compressed, like a pent-up spring, and the last bit of ketchup is pushed out in a sudden blast.

“The splatter of a ketchup bottle can go down to the best of margins: Squeezing very slightly results in a splatter rather than a steady stream of liquid,” Catel said. One helpful tip is to compress slowly, thus reducing the rate of air pressure. Widening the diameter of the nozzle further may help, as the rubber valve on the nozzle can exacerbate the risk of splashing. Granted, valves help avoid threads, but they also force you to create a certain amount of pressure to get the ketchup to start flowing out of the bottle. Cuttle recommends removing the cap from the bottle when it’s almost empty as a practical hack, and squeezing the last bits of ketchup from the wider neck.

“It makes sense, but now there is a rigorous mathematical framework to support it,” Cattell said. “And gas pushing liquid out of the way is something that happens in many other contexts.” This includes aquifers storing trapped carbon dioxide, certain types of volcanic eruptions, and re-inflating of collapsed lungs.

DOI: arXiv, 2022. 10.48550 / arXiv.2112.12898 (About DOIs).